What car should I buy? Details below

Using a throwaway account so my ex doesn't gloat that I am helpless. Folks, I need your help. I am a middle aged single woman living in the Midwest. The clunker I got in the divorce is dying. I am freaking out because I know nothing about cars and have never bought a car myself - was ex used to deal with it. My budget is up to 10K. What car should I buy? What mileage is considered to be good? Where should I look or buy it from? Honestly I am hesitant to go to a dealership - I am worried that cars that got flooded and totaled in the Florida hurricanes may have ended up here.  Any advice is greatly appreciated. Thank you.